Singapore Transit: Transferring Between Terminals

I am flying from Mumbai to Melbourne with a 12.5 hour stopover at Singapore's Changi Airport.

Since it is a codeshare flight between Jet Airways(Mumbai to Singapore) and Qantas(Singapore to Melbourne), I arrive at Terminal 3 and have to depart from Terminal 1.

1) Since the check-in facility for the second leg of my journey begins only 3 hours before departure, and my luggage is through checked-in, I was wondering if I should stay in the Transit area of Terminal 3, or will I be allowed into the Transit Area of Terminal 1 much before my flight departs?